Download Exercise in Control Charts

BA449
Lesson:
Fall 2003
Control Chart Exercises
The exercises below are designed to provide you with some practice in constructing control
charts. Regarding the control charts for attributes, I would like you to do the c chart as well as
the μ chart (lower case Greek letter of Mu and is pronounced the way we spell what a cat says –
mew). Although we did not cover it in class, the μ chart is the more general case of the c chart
and is therefore more versatile. The μ chart is given in your text and student notes. They differ in
that the c chart assumes a constant unit of measurement in the sample being charted, such as the
number of defective stitches per square meter of fabric. The μ chart, on the other hand allows for
a varying sample size. The c chart and μ charts are the most widely used of the attribute charts,
although p charts, which represent the binomial distribution, are still used in some applications,
so it is good to be familiar with p charts as well.
The c chart parameters are given below:
The c chart assumes a Poisson distribution, which is the distribution often followed for rare
events (events that are less than 0.10 of the total population)
c = average number of characteristics (such as defects) per specific unit of measure, such as
square feet, acre, square meter.
__
Standard deviation = √c
The μ chart parameters are given below:
_
μ = process average number of characteristics (such as defects) per unit
n = average sample size
_____
|_
|μ
Standard deviation = √ n
By now, I assume that you are quite familiar with doing the X bar and R charts, so I will not
provide a review here, but will give you some flour data to gain some practice.
Problem: The J. Grout Window Company makes colored-glass objects for home decoration. J.
Grout, the owner, has been concerned about scratches in the finish of recently made products.
The company makes two products, the Poka-Glass, which comes in one standard configuration,
and the Yoka-Glass, which comes in three similar models. Using high-power magnifying
glasses, the company examined 25 each of both the Pokas (one style only) and the Yokas
(randomly selected in all three styles). As Quality Assurance manager, you are asked to evaluate
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the process by determining whether the processes are stable. Note that, on average, the Yokas are
1.5 times the size of the Yokas, so 1.5 represents the average sample size regarding the Yokas.
Assignment: construct the appropriate Statistical Process Control chart for the Poka and Yoka
glass and draw conclusions regarding the control aspects of these processes.
Item Number Poka Defects Yoka Defects
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The Ronib Company is considering purchasing a machine to automatically fill 100 pound bags
with flour. The machine specifications state that the machine is capable of filling bags between
75 to 125 pounds at a standard deviation of 0.18 pounds or less. The specifications state that the
machine error tends to follow a normal distribution, and guarantee that the sample size needed to
do this will be less than 5, with some machines producing an excellent normal distribution such
that running a chart of individuals is sufficient. Other machines necessitate gathering samples in
groups of 2, 3, 4, or 5 before the resulting distribution can be considered normal.
You are the operations manager of the Ronib Company and would be particularly interested in
buying the machines if it not only was able to fill according to specifications. Additionally, it
would be quite desirable if the process could be adequately monitored using a chart of
individuals or a sample size of two or three because it is inconvenient and physically tiring for
the diminutive operator (who weights in at a robust 120 pounds) to have to lift 100 pound sacks
during an eight hours shift. To determine this minimum sample size, the data must be first be
examined on an individual basis and plotted to see if it reasonably follows a normal distribution.
If not, then the sample must be analyzed in groups of 2 i.e. sample size of 2 and that the means of
this grouping should be plotted to determine whether these means follow a normal distribution. If
not, then a sample size of three should be selected. To do this, it will be necessary to construct a
histogram or frequency chart and observe the data to see if it appears to reasonably follow a
normal distribution. Following this, you should construct the appropriate chart(s) to determine
whether the machine will meet your specifications. You have your assistant fill 40 bags with
flour and within a half hour, the assistant places the following data on your desk.
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Sample #
Weight
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99.7
99.6
99.7
99.4
99.4
99.3
99.5
99.8
99.7
99.4
99.6
99.9
99.3
99.2
99.6
99.3
99.5
99.6
99.7
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99.8
99.5
99.4
99.7
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99.7
99.3
99.4
99.5
99.6
99.7
99.2
99.5
99.7
99.6
99.4
99.3
99.5
99.6
When you have finished the assignment, send me an email and I’ll provide the answers.
Ref: C:\ISQA 449\Exercise in Control Charts.doc
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